Dynamical mass generation of a two-component fermion in Maxwell-Chern-Simons QED_3: The lowest ladder approximation

TL;DR

This paper studies how a Chern-Simons term affects dynamical mass generation in QED_3, using the Schwinger-Dyson equation in the lowest ladder approximation, revealing gauge dependence and mass behavior relative to the topological mass.

Contribution

It provides analytical and numerical analysis of dynamical mass generation in QED_3 with a Chern-Simons term, highlighting gauge effects and mass dependence on topological parameters.

Findings

Wave function renormalization close to 1 in Landau gauge

Dynamical mass remains nearly constant when topological mass exceeds coupling

Mass decreases and approaches QED_3 value when topological mass is small

Abstract

Dynamical mass generation of a two-component fermion in $QED_3$ with a Chern-Simons term is investigated by solving the Schwinger-Dyson equation formulated in the lowest ladder approximation. Dependence of the dynamical fermion mass on a gauge-fixing parameter, a gauge coupling constant, and a topological mass is examined by approximated analytical and also numerical methods. The inclusion of the Chern-Simons term makes impossible to choose a peculiar gauge in which a wave function renormalization is absent. The numerical evaluation shows that the wave function renormalization is fairly close to 1 in the Landau gauge. It means that this gauge is still a specific gauge where the Ward-Takahashi identity is satisfied approximately. We also find that the dynamical mass is almost constant if the topological mass is larger than the coupling constant, while it decreases when the topological mass is comparable to or smaller than the coupling constant and tends to the value in $QED_3$ without the Chern-Simons term.